Alex receives 55 emails a day. Out of the 55 emails, 12 emails are spam. If Alex opens 6 emails at random, what is the probability that none of the emails are spam? Enter your answer in decimal form rounded to the nearest thousandths.
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Given : Alex receives 55 emails a day.
Out of the 55 emails, 12 emails are spam.
Alex opens 6 emails at random,
To Find : the probability that none of the emails are spam
Solution:
Total Emails = 55
Spam Emails = 12
Non spam Emails = 55 - 12 = 43
6 Mails out of 55 can be opened in ⁵⁵C₆ ways
6 Mails out of 43 can be opened in ⁴³C₆ ways
probability that none of the emails are spam = ⁴³C₆/⁵⁵C₆
≈ 0.2103
probability that none of the emails are spam is about 0.210
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